A Novel Inverse Filtering-Negative Feedback Low-Frequency Extension Method for Seismic Geophone

To address the challenge of low-frequency seismic signal measurement in ultra-deep oil and gas exploration, an inverse filtering-negative feedback low-frequency extension (IF-NF-LFE) method is proposed based on the negative feedback closed-loop (NFCL) model. An adjustable negative feedback circuit (ANFC) is firstly designed by incorporating tunable resistors. For the NFCL model comprising the ANFC and geophone electromagnetic dynamics model, the system transfer function is derived through the force-balance principle, followed by analysis of system consistency performance and frequency response characteristics. Theoretically cascading an ideal inverse filter can ensure voltage-velocity linearity but exhibit complex circuit and notable low-frequency inherent noise. Consequently, an approximate transfer function is constructed via the least-squares algorithm to asymptotically approach the ideal inverse filter, and the stability of the IF-NF-LFE system is analyzed. Finally, we implement the extension circuit, and propose a dual-frequency calibration strategy to optimize the consistency of sensitivity and cutoff frequency. Using the proposed method, a low-frequency extension circuit is designed for a 5 Hz moving-coil geophone, and its performance (sensitivity of 200 V/(m·s⁻¹) ±5%, corner frequency extended to 0.2 Hz ±5%, consistency and noise floor) is validated through standard vibration table testing. Furthermore, a small batch of compact and rugged integrated low-frequency geophones are manufactured, with multiple comparative verification tests performed under field conditions.